A258823 Numbers m such that k iterations of m under the '3x+1' map yield k for some k.
2, 7, 8, 10, 18, 19, 24, 26, 41, 43, 44, 45, 46, 48, 52, 53, 64, 65, 66, 67, 72, 74, 76, 77, 97, 98, 99, 100, 101, 102, 112, 116, 117, 120, 122, 144, 148, 149, 153, 156, 157, 158, 160, 172, 173, 174, 175, 209, 210, 211, 246, 247, 248, 249, 250, 252, 253, 254, 255, 260, 261, 262, 264, 266, 268, 269, 272
Offset: 1
Keywords
Examples
For m = 6, the '3x+1' map is as follows: 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. For any possible k, after the k-th iteration, the result does not equal k. Thus 6 is not a member of this sequence. For m = 7, the '3x+1' map is as follows: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. After 10 iterations, we arrive at 10. So, 7 is a member of this sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
kQ[n_]:=Module[{tr=Rest[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n, #>1&]], len}, len = Length[ tr];Count[Thread[{tr,Range[len]}],?(#[[1]] == #[[2]]&)]>0]; Select[Range[300],kQ] (* _Harvey P. Dale, Jan 13 2017 *) -
PARI
Tvect(n)=v=[n]; while(n!=1, if(n%2, k=3*n+1; v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v n=1;while(n<10^3,d=Tvect(n); c=0; for(i=1, #d, if(d[i]==i-1,print1(n, ", ");break));n++)
Comments